Let y = x² − 4x. Substitute y into the expression.

Question

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To simplify the expression (x² − 4x + 4)(x² − 4x) + 3, we will expand the product and then combine like terms. Step 1: Let y = x² − 4x. Substitute y into the expression. The expression becomes (y + 4)y + 3. Step 2: Expand the expression in terms of y. (y + 4)y + 3 = y² + 4y + 3; Step 3: Substitute y = x² − 4x back into the expanded expression. (x² − 4x)² + 4(x² − 4x) + 3 Step 4: Expand (x² − 4x)² using the formula (a−b)² = a² − 2ab + b². Here, a = x² and b = 4x. (x² − 4x)² = (x²)² − 2(x²)(4x) + (4x)² = x⁴ − 8x³ + 16x² Step 5: Expand 4(x² − 4x). 4(x² − 4x) = 4x² − 16x Step 6: Combine all the expanded terms. (x⁴ − 8x³ + 16x²) + (4x² − 16x) + 3 Step 7: Combine like terms. x⁴ − 8x³ + (16x² + 4x²) − 16x + 3 x⁴ − 8x³ + 20x² − 16x + 3 The simplified expression is: x⁴ − 8x³ + 20x² − 16x + 3

Point	x	y
x-intercept	0	0
Minimum	2	−4
x-intercept	4	0

Let y = x² − 4x. Substitute y into the expression.

Answer

Step-by-step solution

Let $y = x^2 - 4x$ .

Expand the expression in terms of $y$ .

Substitute $y = x^2 - 4x$ back into the expanded expression.

Expand $(x^2 - 4x)^2$ using the formula $(a-b)^2 = a^2 - 2ab + b^2$ .

Expand $4(x^2 - 4x)$ .

Combine all the expanded terms.

Combine like terms.

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More Mathematics Questions

Let y = x² − 4x. Substitute y into the expression.

Answer

Step-by-step solution

Let y=x2−4xy = x^2 - 4xy=x2−4x.

Expand the expression in terms of yyy.

Substitute y=x2−4xy = x^2 - 4xy=x2−4x back into the expanded expression.

Expand (x2−4x)2(x^2 - 4x)^2(x2−4x)2 using the formula (a−b)2=a2−2ab+b2(a-b)^2 = a^2 - 2ab + b^2(a−b)2=a2−2ab+b2.

Expand 4(x2−4x)4(x^2 - 4x)4(x2−4x).

Combine all the expanded terms.

Combine like terms.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Let $y = x^2 - 4x$ .

Expand the expression in terms of $y$ .

Substitute $y = x^2 - 4x$ back into the expanded expression.

Expand $(x^2 - 4x)^2$ using the formula $(a-b)^2 = a^2 - 2ab + b^2$ .

Expand $4(x^2 - 4x)$ .